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Shouhong Wang
Stochastic Parameterizing Manifolds and Non-Markovian Reduced Equations
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4054032Stochastic Parameterizing Manifolds and Non-Markovian Reduced Equationshttps://www.gandhi.com.mx/stochastic-parameterizing-manifolds-and-non-markovian-reduced-equations-9783319125206/phttps://gandhi.vtexassets.com/arquivos/ids/2563384/23790e59-a38c-4efb-8069-00e108d8519d.jpg?v=6383841450501700009761084MXNSpringer International PublishingInStock/Ebooks/<p>In this second volume, a general approach is developed to provide approximate parameterizations of the "small" scales by the "large" ones for a broad class of stochastic partial differential equations (SPDEs). This is accomplished via the concept of parameterizing manifolds (PMs), which are stochastic manifolds that improve, for a given realization of the noise, in mean square error the partial knowledge of the full SPDE solution when compared to its projection onto some resolved modes. Backward-forward systems are designed to give access to such PMs in practice. The key idea consists of representing the modes with high wave numbers as a pullback limit depending on the time-history of the modes with low wave numbers. Non-Markovian stochastic reduced systems are then derived based on such a PM approach. The reduced systems take the form of stochastic differential equations involving random coefficients that convey memory effects. The theory is illustrated on a stochastic Burgers-type equation.</p>...3989912Stochastic Parameterizing Manifolds and Non-Markovian Reduced Equations9761084https://www.gandhi.com.mx/stochastic-parameterizing-manifolds-and-non-markovian-reduced-equations-9783319125206/phttps://gandhi.vtexassets.com/arquivos/ids/2563384/23790e59-a38c-4efb-8069-00e108d8519d.jpg?v=638384145050170000InStockMXN99999DIEbook20149783319125206_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9783319125206_<p>In this second volume, a general approach is developed to provide approximate parameterizations of the small scales by the large ones for a broad class of stochastic partial differential equations (SPDEs). This is accomplished via the concept of parameterizing manifolds (PMs), which are stochastic manifolds that improve, for a given realization of the noise, in mean square error the partial knowledge of the full SPDE solution when compared to its projection onto some resolved modes. Backward-forward systems are designed to give access to such PMs in practice. The key idea consists of representing the modes with high wave numbers as a pullback limit depending on the time-history of the modes with low wave numbers. Non-Markovian stochastic reduced systems are then derived based on such a PM approach. The reduced systems take the form of stochastic differential equations involving random coefficients that convey memory effects. The theory is illustrated on a stochastic Burgers-type equation.</p>(*_*)9783319125206_<p>In this second volume, a general approach is developed to provide approximate parameterizations of the "small" scales by the "large" ones for a broad class of stochastic partial differential equations (SPDEs). This is accomplished via the concept of parameterizing manifolds (PMs), which are stochastic manifolds that improve, for a given realization of the noise, in mean square error the partial knowledge of the full SPDE solution when compared to its projection onto some resolved modes. Backward-forward systems are designed to give access to such PMs in practice. The key idea consists of representing the modes with high wave numbers as a pullback limit depending on the time-history of the modes with low wave numbers. Non-Markovian stochastic reduced systems are then derived based on such a PM approach. The reduced systems take the form of stochastic differential equations involving random coefficients that convey memory effects. The theory is illustrated on a stochastic Burgers-type equation.</p>...9783319125206_Springer International Publishinglibro_electonico_fcefacf6-c575-3a06-8049-d1ec80089e4c_9783319125206;9783319125206_9783319125206Shouhong WangInglésMéxico2014-12-23T00:00:00+00:00Springer International Publishing